Perhaps the most successful revolver cartridge of all time, the .38 Special is most at home in a small-frame, concealable revolver and exhibits performance in ballistic gelatin similar, but not quite equal to the 9x19mm Luger.
Commonly available jacketed hollowpoints (JHPs) in this caliber will generally exhibit above-average bullet expansion and slightly-less than 12" penetration depths, when fired from a short-barreled revolver (a 'snub nose'). This is largely due to the fact that the longer a gun barrel is, more of the bullets propellant charge is burned and the faster the bullet travels. Snub nose revolvers typically utilize 2" long barrels, among the shortest barrel lengths for any caliber handgun, exacerbating this situation.
For longer barrel lengths (which usually means a larger gun in terms of all the other dimensions - weight and height, etc), a .357 Magnum is recommended. This handgun can fire the .38 Special (with no additional safety precautions) and of course, the much more effective Magnum load. Such a cartridge/gun combination can easily be handled by a shooter of moderate handgun experience and ammunition for both calibers is widely available at a reasonable cost.